Number System

Question 1
If the numerical value of a 2-byte unsigned integer on a little endian computer is 255 more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer?
[MSQ]
A
0x6665
B
0x0001
C
0x4243
D
0x0100
GATE CSE 2021 SET-2   Digital Logic
Question 2
If x and y are two decimal digits and (0.1101)_2 = (0.8xy5)_{10}, the decimal value of x+y is ___________
A
3
B
6
C
8
D
4
GATE CSE 2021 SET-2   Digital Logic
Question 3
The format of the single-precision floating point representation of a real number as per the IEEE 754 standard is as follows:

\begin{array}{|c|c|c|} \hline \text{sign} & \text{exponent} & \text{mantissa} \\ \hline \end{array}

Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?
A
exponent = 00000000 and mantissa = 0000000000000000000000000
B
exponent = 00000000 and mantissa = 0000000000000000000000001
C
exponent = 00000001 and mantissa = 0000000000000000000000000
D
exponent = 00000001 and mantissa = 0000000000000000000000001
GATE CSE 2021 SET-2   Digital Logic
Question 4
Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S:1
E:10000001
F:11110000000000000000000

Here, S,E and F denote the sign, exponent, and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is ____________.
A
-7.75
B
7.75
C
-3.825
D
3.825
GATE CSE 2021 SET-1   Digital Logic
Question 5
Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?
A
15
B
21
C
D2
D
528
GATE CSE 2021 SET-1   Digital Logic
Question 6
Consider three registers R1, R2, and R3 that store numbers in IEEE-754 single precision floating point format. Assume that R1 and R2 contain the values (in hexadecimal notation) 0x42200000 and 0xC1200000, respectively.

If R3=\frac{R1}{R2}, what is the value stored in R3?
A
0x40800000
B
0xC0800000
C
0x83400000
D
0xC8500000
GATE CSE 2020   Digital Logic
Question 7
Consider Z = X - Y where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of Z would require a minimum of:
A
n bits
B
n-1 bits
C
n+1 bits
D
n+2 bits
GATE CSE 2019   Digital Logic
Question 8
In 16-bit 2's complement representation, the decimal number -28 is:
A
1111 1111 0001 1100
B
0000 0000 1110 0100
C
1111 1111 1110 0100
D
1000 0000 1110 0100
GATE CSE 2019   Digital Logic
Question 9
A computer uses ternary system instead of the traditional systen, An n bit string in the binary system will occupy
A
3+n ternary digits
B
2n/3 ternary digits
C
n \log _{2} 3 ternary digits
D
n \log _{3} 2 ternary digits
ISRO CSE 2018   Digital Logic
Question 10
Given \sqrt{224_{r}}=13_{r} the value of radix r is
A
10
B
8
C
6
D
5
ISRO CSE 2018   Digital Logic
There are 10 questions to complete.

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